Solve a^2-9b^2/a^2-ab:a^2+3a/a-b

$$\frac { a ^ { 2 } - 9 b ^ { 2 } } { a ^ { 2 } - a b } : \frac { a ^ { 2 } + 3 a } { a - b }$$

Evaluate

$$\frac{a^{2}-9b^{2}}{\left(a+3\right)a^{2}}$$

Short Solution Steps

Divide \frac{a^{2}-9b^{2}}{a^{2}-ab} by \frac{a^{2}+3a}{a-b} by multiplying \frac{a^{2}-9b^{2}}{a^{2}-ab} by the reciprocal of \frac{a^{2}+3a}{a-b}.

$$\frac{\left(a^{2}-9b^{2}\right)\left(a-b\right)}{\left(a^{2}-ab\right)\left(a^{2}+3a\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-3b\right)\left(a-b\right)\left(a+3b\right)}{\left(a+3\right)\left(a-b\right)a^{2}}$$

Cancel out a-b in both numerator and denominator.

$$\frac{\left(a-3b\right)\left(a+3b\right)}{\left(a+3\right)a^{2}}$$

Expand the expression.

$$\frac{a^{2}-9b^{2}}{a^{3}+3a^{2}}$$

Expand

$$\frac{a^{2}-9b^{2}}{a\left(a^{2}+3a\right)}$$

Short Solution Steps

Divide \frac{a^{2}-9b^{2}}{a^{2}-ab} by \frac{a^{2}+3a}{a-b} by multiplying \frac{a^{2}-9b^{2}}{a^{2}-ab} by the reciprocal of \frac{a^{2}+3a}{a-b}.

$$\frac{\left(a^{2}-9b^{2}\right)\left(a-b\right)}{\left(a^{2}-ab\right)\left(a^{2}+3a\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a-3b\right)\left(a-b\right)\left(a+3b\right)}{\left(a+3\right)\left(a-b\right)a^{2}}$$

Cancel out a-b in both numerator and denominator.

$$\frac{\left(a-3b\right)\left(a+3b\right)}{\left(a+3\right)a^{2}}$$

Expand the expression.

$$\frac{a^{2}-9b^{2}}{a^{3}+3a^{2}}$$